Question

Sam and Kevin both worked hard over the summer. Together they earned a total of $425. Kevin earned $ 25 more than Sam.

a) Write a system of equations for the situation. Use s for the amount Same earned and k for the amount Kevin earned.
b) Graph the equations in the system.
c) Use your graph to estimate how much each person earned.


Solve the system of equations by substitution.
6= -4x + Y
-5x - Y =21

Solve the system by the elimination method.
2x + y=20
6x - 5y=12

Please help I do not understand how to do this ..Thanks

Answer 1

QUESTION 1

a)

Let

`s`

represent the amount Same earned and

`k`

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

`k+s= 425---eqn(1)`

It was also given that, Kevin earned $25 more than Same.

This implies,

`k-s=25---eqn(2)`

For equation (1), when

`s=0`

`k=425`

We plot the point,

`(425,0)`

When

`k=0`

`s=425`

We plot the point,

`(0,425)`

Similarly for the second equation when

`s=0`

`k=25`

This gives the point,

`(25,0)`

When

`k=0`

`s=-25`

We plot

`(0,-25)`

and draw a straight line through them.

We can see from the graph that the two points intersect at

`(225,200)`

This implies that

`k=225\:and\:s=200`

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

`6=-4x + y---eqn(1)`

and

`-5x-y=21---eqn(2)`

From equation (2),

`y=-5x-21---eqn(3)`

Put equation (3) into equation (1).

This implies that,

`6=-4x-5x-21`

Group like terms,

`6+21=-4x-5x`

Simplify, to get,

`27=-9x`

`x=-3`

We substitute this value into equation (3) to get,

`y=-5(-3)-21`

`y=15-21`

`y=-6`

Therefore the solution is

`(-3,-6)`

QUESTION 3

We want to solve,

`2x+y=20---(1)`

and

`6x -5y=12---(2)`

We multiply equation (1) by 3 to get,

`6x+3y=60---(3)`

Equation (3) minus equation (2) will give us,

`8y=48`

This means

`y=6`

Put this value into equation (1) to get,

`2x+6=20`

`2x=20-6`

`2x=14`

`x=7`

The solution is

`(7,6)`

Answer 2

Sam earns $200 and Kevin earns $225.

x , y= -3 , -6 by substitution

x , y= 7, 6 by elimination

Explanation:

a) Let the amount earned by Sam = s and the amount earned by Kevin = k

We are given, that they both earn total $425 i.e. s + k = 425

Also, Kevin earns $25 more than Sam i.e. k = s + 25

Hence, the system of equations comes out to be:

s + k = 425

-s + k = 25

b) Take s = x and k = y. See the graph plotted below

c) As the intersection point from the graph comes out to be (s,k) = (200,225)

Therefore, Sam earns $200 and Kevin earns $225.

Now, we have the system

-4x + y = 6

-5x - y = 21

We need to use substitution method.

Take y= -5x - 21 from the 2nd equation and put it in the 1st.

We get, -4x - 5x - 21 = 6 i.e. -9x = 27 i.e. x= -3

Now, substitute this value of x in any of the equation to find y.

We get, -5*(-3) - y = 21 i.e. y = 15 - 21 i.e. y = -6

Now, we are given the system,

2x + y = 20

6x - 5y = 12

We need to use elimination method.

Multiply 5 by equation 1. We get,

10x + 5y = 100

6x - 5y = 12

Adding the above equations, we get, 16x = 112 i.e. x = 7

Put this value in any of the equation to find the value of y.

We get, y = 20 - 2x i.e. y = 20 - 2*7 i.e. y = 20 - 14 i.e. y = 6